140
Robert J Hill
Inflation Measurement for Central Bankers
Robert J Hill
1.
Introduction
Interest in the measurement of inflation has increased significantly in recent years
for a number of reasons. First, inflation rates have fallen significantly since the early
1980s. Second, many central banks have adopted inflation targets. The combination
of these two factors has increased the importance of accurate measurement. Third,
rapid quality improvements, particularly in the information technology and health
sectors, have made accurate measurement more difficult. The final impetus was
provided by the Boskin et al (1996) report which claimed that the US consumer
price index (CPI) has an upward bias in excess of 1 percentage point per year,
while at the same time pointing out the dramatic budgetary implications of this
bias, which arises from the fact that about one-third of federal expenditure in the
US is indexed to the CPI.
Most central banks that have adopted inflation targets have been very successful
in getting their inflation rates down to historically low levels. It is important to
remember, nevertheless, that inflation is a surprisingly slippery concept. It is not
clear exactly what concept of inflation is most relevant in a central banking context,
or how it can best be measured. For example, should we focus on consumer, producer
and/or asset prices? Even if we agree on consumer prices, should some volatile
or hard-to-measure categories such as food, energy or owner-occupied housing
be excluded? Also, in a consumer context, a distinction can be drawn between
a cost of goods (and services) index (COGI) and a cost of living index (COLI).
Adjustments must be made for quality change and new goods and services, which
the Boskin et al (1996) report identifies as the main source of bias in the US CPI.
Such adjustments require econometric estimation of hedonic models. It is important
to factor in estimates of possible biases when setting an inflation target, and for
central banks to account for new statistical innovations introduced by national
statistical offices to reduce these biases. It is not clear how frequently the index
should be computed or how often it should be rebased. The increased availability
of scanner data has the potential to revolutionise the construction of consumer price
indices, allowing them to be computed more frequently using expenditure weights
at a much finer level of aggregation than is currently possible. However, the use of
scanner data may also increase the volatility of the CPI, an eventuality that might
not be welcome in central banking circles.
This paper surveys these issues. My objective is not so much to provide answers
as it is to alert users of inflation targets to the underlying complexities of the inflation
concept itself. These issues bear directly on the choice of the inflation target and on
how a central bank should respond to changes in the observed rate of inflation.
Inflation Measurement for Central Bankers
2.
141
The Choice of Target
Most central banks target the CPI. However, it is not the only readily available
measure of inflation in an economy. In particular, two notable alternatives are the
producer price index (PPI) and gross domestic product (GDP) deflator. To decide
which concept provides the most appropriate inflation target, it is useful to step
back and consider why inflation is a problem in the first place. One significant cost
of inflation is that it distorts the scarcity signals in relative price movements. This
is, at least partly, attributable to the fact that, by trying to reduce menu costs, firms
do not continuously adjust their prices. This leads to relative price movements
with no information content that become more pronounced as the inflation rate
rises. Empirically, a number of authors have demonstrated the positive correlation
between the inflation rate and relative price variability (see, for example, Silver and
Ioannidis 2001). This noise in relative price movements can lead to a misallocation
of investment funds as well as discouraging investment by causing uncertainty. In
addition, Feldstein (1997) argues that inflation reduces the after-tax real rate of interest
and affects the after-tax return on some assets more strongly than others, thus further
distorting investment and savings decisions. Given the emphasis in these arguments
on investment, which is excluded from the domain of the CPI, this suggests that
it may be better for a central bank to target the PPI or GDP deflator. However, the
coverage of the PPI is quite narrow, focusing mainly on the manufacturing sector
(see the International Monetary Fundʼs PPI manual, 2004). Hence, it is probably
not a suitable target. Likewise, Kohli (1983) and Diewert (2002) note how the fact
that import quantities have negative weights in the GDP deflator implies that a rise
in import prices acts directly to reduce the GDP deflator. Hence, the GDP deflator
is also unsuitable as an inflation target. Diewert goes on to consider a number of
variants on the GDP deflator, such as deflators for C+I+G+X, C+I+G and C+G.
TP Hill (1996), Woolford (1999) and Bloem, Armknecht and Zieschang (2002)
advocate deflators for either C+I+G+X or C+I+G, while Diewert (1996) advocates
the deflator for C+G on the grounds that prices for capital expenditure are not
relevant to the deflation of current period household expenditures. He then argues
that G should also be deleted due to the difficulty of obtaining meaningful prices
for items of government expenditure. Hence, he concludes that the CPI is perhaps
the best measure of inflation.
An additional argument in favour of the CPI as an inflation target is that it is
the standard benchmark used by employees and employers in wage negotiations
and is used to index public sector wages and pensions. To the extent that inflation
is of the wage cost-push variety, a central bank should, therefore, target the CPI
since this will directly impact inflationary expectations and hence wages. In fact,
in most countries the CPI was developed as a benchmark against which public
sector wages and pensions could be indexed. It was only subsequently that the CPI
was adopted by central banks as an inflation target. In some countries, this has led
to changes in the CPI, for example the exclusion of mortgage interest payments
from the Australian CPI. One important exception from this general pattern is the
European Unionʼs Harmonised Index of Consumer Prices (HICP), which has been
142
Robert J Hill
constructed specifically as an inflation target (for the European Central Bank). The
HICP is discussed in greater detail later in the paper (also see Diewert 2002).
There has been much debate recently over whether asset prices should be included
in an inflation target (see, for example, Goodhart 2001 and Tatom 2002). The current
target, the CPI, includes one of the most important assets, that is, owner-occupied
housing, although in Australia and New Zealand only the cost of the building
materials and labour are included (this point is discussed in more detail later in
the paper). It also includes consumer durables, such as cars. However, it excludes
most financial assets (e.g. stocks), as do all other currently available measures of
inflation. The treatment of asset prices tends to attract most attention during periods
when asset and consumer price movements diverge from each other, as happened in
Japan in the late 1980s and the US in the late 1990s. The concern is that when asset
prices rise faster than consumer prices, this will ultimately feed back into consumer
prices. It does not follow, however, that asset prices should necessarily be included
in the target index. Rather, the more natural implication is that central banks should
plan ahead and engage in inflation forecasting as part of their inflation-targeting
strategy. Asset prices are an important input into this process.
It is sometimes argued that food and energy prices should be excluded from
the inflation target. There are two main justifications for this argument. First,
Blinder (1997) argues that in the US, food and energy prices are largely beyond
the control of the Federal Reserve. I find this argument surprising. Even if food
and energy prices are beyond the control of the Federal Reserve, it does not follow
that they should be ignored. It may still be desirable to try and make adjustments
elsewhere in the economy so as to keep the CPI in an acceptable range. Second,
it is generally believed that the inclusion of certain food items, such as fresh fruit
and vegetables, and energy items, such as petrol, makes the CPI more volatile.
Cecchetti (1997) casts some doubt on this claim. Again, even if this is true, it does
not follow that these very important components of consumer expenditure should
be excluded from the inflation target. What it suggests is that a central bank should
be allowed to take a reasonably long-term view with regard to meeting its inflation
target. A central bank should not be expected to respond aggressively to every
short-run fluctuation in the CPI. Clearly, there is a role for core inflation measures to
help determine the direction of the underlying inflation rate by separating transitory
shocks from long-run trends (see Cecchetti 1997). However, this does not mean
that a core inflation measure should become the target itself.
3.
The COGI versus COLI Debate
Even if it is agreed that the focus of attention is consumer expenditure, this does
not resolve all conceptual ambiguities. The CPI could be defined as measuring the
cost of buying a particular basket of goods and services or as the cost of achieving
a given level of utility. A distinction has, therefore, been drawn in the consumer
price index literature between a cost of goods index (COGI) and a cost of living
index (COLI).
Inflation Measurement for Central Bankers
143
The main issue for a COGI is the choice of reference basket. Let pt denote the
price vector of period t (the base period), and pt+k the price vector of period t+k
(the current period). If the base periodʼs basket (that is, qt) is used, we obtain a
Laspeyres price index. If the current periodʼs basket is used (that is, qt+k), we obtain
a Paasche price index. Let n = 1,..., N index the goods and services included in the
reference basket. It is assumed here that the goods and services under consideration
do not change between periods t and t+k. The treatment of new goods and quality
change are discussed later in the paper. The price of good n in period t is denoted
by pt,n while the quantity of good n in the reference basket of period t is denoted by
qt,n. The Laspeyres and Paasche indices are defined as follows:
Σ nN=1 pt + k , n qt , n
Σ nN=1 pt , n qt , n
(1)
Σ nN=1 pt + k , n qt + k , n
Σ nN=1 pt , n qt + k , n
(2)
Laspeyres: Pt ,Lt + k =
Paasche: Pt P, t + k =
The problem with both of these indices is that they suffer from representativity
bias (see TP Hill 1998). That is, to correctly measure the change in the price level,
the reference basket should be representative of the two periods being compared.
This problem can be dealt with by using a reference basket that is an average of
the baskets of the two periods being compared. Two such indices have received
attention in the price index literature.
Marshall-Edgeworth: Pt ,ME
t+k =
W
t ,t + k
Walsh: P
=
Σ nN=1 pt + k , n ( qt , n + qt + k , n )
Σ nN=1 pt , n ( qt , n + qt + k , n )
Σ nN=1 pt + k , n qt , n qt + k , n
(3)
(4)
Σ nN=1 pt , n qt , n qt + k , n
Alternatively, instead of constructing an average basket, we could take an average
of Laspeyres and Paasche indices. This is the approach followed by the Fisher index,
which is a geometric mean of Laspeyres and Paasche indices.
Fisher: Pt F, t + k = Pt ,Lt + k Pt P, t + k
(5)
A price index can also be constructed by taking a geometric mean of price ratios.
The geometric Laspeyres index weights each price ratio by its expenditure share in
the base period, while the geometric Paasche index weights each price ratio by its
expenditure share in the current period. By taking a geometric mean of geometric
Laspeyres and geometric Paasche indices we obtain the Törnqvist index.
GL
t ,t + k
Geometric Laspeyres: P
GP
t ,t + k
Geometric Paasche: P
⎛p
⎞
= Π ⎜ t + k,n ⎟
n =1
⎝ pt , n ⎠
N
⎛p
⎞
= Π ⎜ t + k,n ⎟
n =1
⎝ pt , n ⎠
N
st ,n
(6)
st + k ,n
(7)
144
Robert J Hill
Tornqvist:
PtT, t + k
©p
¹
= 5 ª t + k,n º
n =1
« pt , n »
N
( st ,n + st + k ,n )
2
(8)
The term st,n denotes the expenditure share of good n in period t:
N
st , n = pt , n qt , n ⎛ Σ pt , i qt , i ⎞
⎝ i =1
⎠
(9)
To avoid representativity bias, one out of the Marshall-Edgeworth, Walsh, Fisher
and Törnqvist indices should be used. These indices will tend to approximate each
other quite closely, so the choice between them is of limited practical significance.
If required, the axiomatic approach to index numbers can be used to discriminate
between them. Usually the formula that emerges as best from an axiomatic perspective
is the Fisher index. In particular, it is the only one of these formulae that satisfies the
factor reversal test (see Balk 1995). Nevertheless, in some circles these four indices
are viewed with suspicion. Von der Lippe (2001), in particular, strongly advocates
the Laspeyres index on the grounds that it is easier to interpret since it has a fixed
reference basket. Among academic researchers, his is a minority position.
A COLI (see Konüs 1939) takes the following form:
COLI t , t + k =
e ( pt + k , u )
e ( pt , u )
(10)
where e(p, u) is an expenditure function which measures the minimum expenditure
required to reach the utility level u given prices p. There are three main problems
with the concept of a COLI. First, it depends on the reference utility level. Second, it
assumes the existence of a representative agent. Last, but not least, it is not directly
observable. We will consider each of these problems in turn.
The COLI is independent of the reference utility level only if preferences are
homothetic. Clearly, in practice, preferences are not homothetic. This suggests that
rich and poor people face different rates of inflation. Intuitively, this is not surprising
since they buy different baskets of goods and services. For example, the price of a
yacht may be a matter of concern to a rich person, but it is of complete irrelevance
to a poor person. People also have different tastes. Part of this difference can be
attributed to age differences. For example, the price of a hip replacement matters
more to a retiree than to someone in their twenties. This brings into question the
assumption of a representative agent. Attempts have been made to broaden the
concept of a COLI to groups (see Pollak 1981). However, it is hard to see how this
concept could be implemented in practice (see Deaton 1998).
Although the COLI is not directly observable, it is bounded from below given
the reference price vector pt+k by Paasche, and from above given the reference price
vector pt by Laspeyres. Paasche and Laspeyres bound the COLI because they fail
to take account of the fact that consumers change their consumption patterns when
relative prices change, switching from goods that have become relatively more
expensive to goods that have become relatively cheaper. In other words, Paasche and
Inflation Measurement for Central Bankers
145
Laspeyres indices are both subject (in opposite directions) to substitution bias. The
substitution bias of Paasche and Laspeyres indices in a COLI context is analogous
to the representativity bias of Paasche and Laspeyres indices in a COGI context.
When preferences are homothetic, Paasche and Laspeyres indices provide lower
and upper bounds, respectively, on the same COLI. It can be argued, therefore, that
the geometric mean of Laspeyres and Paasche (that is, Fisher) should approximate
reasonably closely the underlying COLI. Alternatively, under the assumption of
utility maximising behaviour, once a functional form has been specified for the
expenditure function, the COLI reduces to a function of observable prices and
quantities. In fact, each price index formula is exact (that is, equals the COLI) for
a particular expenditure function. For example, the Törnqvist index is exact for the
translog expenditure function, while the Fisher index is exact for the normalised
quadratic expenditure function. Diewert (1976) argued that we should prefer price
index formulae that are exact for flexible expenditure functions (that is, expenditure
functions that are twice continuously differentiable and can approximate an
arbitrary linearly homogeneous function to the second order). He referred to price
indices that satisfy this condition as superlative. Diewert went on to identify a family
of superlative formulae of the following form:1
r
t ,t + k
P
=
N
r /2 ⎞
⎛Σ
/p
s p
⎝ n =1 t , n ( t + k , n t , n ) ⎠
1/ r
N
−r /2
⎛Σ
st + k , n ( pt + k , n / pt , n ) ⎞
⎝ n =1
⎠
1/ r
r ≠ 0,
0
t ,t + k
P
st ,n + st + k ,n
⎡
2
⎛
⎞
p
⎢
= Π ⎢⎜ t + k , n ⎟
n =1
⎝ pt , n ⎠
⎢⎣
N
⎤
⎥
⎥ (11)
⎥⎦
where st,n denotes the expenditure share of product n in time period t as defined in
Equation (9). A second class of superlative price indices is derived implicitly as
follows:
Pt r, t + k =
1
Qtr, t + k
8 nN=1 pt + k , n qt + k , n
8 nN=1 pt , n qt , n
(12)
where Qtr, t + k denotes the corresponding family of superlative quantity indices
defined below.
r
t ,t + k
Q
=
N
r /2
⎛Σ
st , n ( qt + k , n / qt , n ) ⎞
⎝ n =1
⎠
1/ r
N
−r /2 ⎞
⎛Σ
s
q
/q
⎝ n =1 t + k , n ( t + k , n t , n ) ⎠
1/ r
r ≠ 0,
0
t ,t + k
Q
st ,n + st + k ,n
⎡
⎢⎛ qt + k , n ⎞ 2
= Π ⎢⎜
⎟
n =1
⎝ q ⎠
⎢⎣ t , n
N
⎤
⎥ (13)
⎥
⎥⎦
Although there are an infinite number of superlative price indices, since the
parameter r can take any finite positive or negative value, only three simplify in
1
an intuitively appealing manner: Pt 0, t + k is the Törnqvist price index, Pt , t + k is the
2
Walsh price index, and Pt , t + k is the Fisher price index. It should be noted that none
of Laspeyres, Paasche, Marshall-Edgeworth, geometric Laspeyres and geometric
1. The limit of the superlative formula as r tends to zero is the Törnqvist price index. If Equation (11)
is defined for r = 0 as in the Törnqvist price index, the function is continuous on the real line.
146
Robert J Hill
Paasche indices are superlative. It is interesting that these same three formulae (Fisher,
Walsh and Törnqvist) are the three that usually emerge as best from an axiomatic
perspective. Furthermore, for most data sets, the Fisher, Walsh and Törnqvist indices
approximate each other closely (although it is not true that all superlative indices
approximate each other closely; see RJ Hill forthcoming). Whatever the starting
point, therefore, the outcome is similar.
This seems to imply that the choice between a COGI and COLI is of merely
academic interest. While this is true with regard to the choice of formula, it is not true
more generally, since the COGI versus COLI stance taken by a national statistical
office is a signal of intent with regard to imputations. A statistical office that favours
the COLI concept is likely to quality-adjust its CPI more than a statistical office
that favours the COGI concept. The stance taken in the COGI versus COLI debate
may also impact on the treatment of owner-occupied housing. These issues are
discussed later in the paper.
The analysis thus far ignores environmental variables that affect utility such
as climate, air quality, the crime rate and the divorce rate. If these are allowed
to vary when computing the COLI, this drives a wedge between the COGI and
COLI concepts. This is because, by construction, a COGI does not respond to
such environmental variables. At this point a distinction must be drawn between a
conditional and unconditional COLI (see Pollak 1989). To illustrate this distinction,
an extra term z denoting environmental variables must be added to the definition of
a COLI in Equation (10). An unconditional COLI, denoted here by COLI U, allows
z to vary over time.
e ( pt + k , zt + k , u )
COLI tU, t + k =
(14)
e ( pt , zt , u )
By contrast, a conditional COLI, denoted here by COLI C, holds z fixed.
e ( ( pt + k , z, u )
COLI tC, t + k =
e ( pt , z, u )
(15)
For a conditional COLI this then raises the question of whether zt or zt+k as well as ut
or ut+k should be used as the reference. This decision is analogous to the one faced
by a COGI with regard to the choice of reference basket (qt or qt+k ). Both a COGI
and a conditional COLI should only respond to movements in the quality-adjusted
prices of goods and services (appropriately weighted by expenditure shares). An
unconditional COLI, by contrast, will respond to changes in environmental variables
even if the prices of all goods and services remain fixed. It would make no sense,
therefore, for a central bank to target an unconditional COLI. For example, suppose
the divorce rate rises. This, other things equal, will increase an unconditional COLI.
As a result, a central bank targeting an unconditional COLI might have to respond
to this by raising interest rates. Clearly, monetary policy should only respond to
changes in the prices of goods and services. Furthermore, the use of an unconditional
COLI would introduce a huge number of dubious imputations into the CPI (such
as placing a dollar value on the change in the divorce rate).
Inflation Measurement for Central Bankers
147
Which concept out of a COGI and a conditional COLI provides the most
appropriate inflation target for a central bank? The Statistical Office of the European
Union (Eurostat) has stated clearly that the HICP is not a COLI (see Astin 1999 and
Diewert 2002), as has the Australian Bureau of Statistics (ABS) with regard to the
Australian CPI (see ABS 2000). In contrast, the Bureau of Labor Statistics (BLS)
has adopted the COLI concept for the US CPI (see Triplett 2001). Triplett (2001)
emphatically argues that the CPI should be based on the COLI concept. However, he
is unduly harsh in his criticism of the COGI since he seems to equate a COGI with
a Laspeyres index. This is not necessarily the case. In a COGI setting, a Laspeyres
index is still subject to representativity bias. Also, the axiomatic approach can be
equally well applied to the COGI concept as to the COLI concept. Nevertheless, I
agree with Triplett that a central bank should not be targeting a Laspeyres index. The
target should be calculated using one of the Fisher, Walsh or Törnqvist formulae.
This conclusion, however, can be reached from either the COGI or constrained
COLI perspective.
Even statistical offices that advocate the COLI concept are more or less forced to
use a Laspeyres index due to the fact that expenditure weights for the current period
are typically not available when the CPI is released. In fact, to be more precise, the
index actually used typically is not even Laspeyres. This is because the expenditure
weights in the CPI are drawn from one or more years, while the CPI is computed
monthly or quarterly (depending on the country). The formula actually used is a
Lowe index, which is defined below.
Lowe: Pt ,Low
t+k =
Σ nN=1 pt + k , n q X , n
Σ nN=1 pt , n q X , n
(16)
The important thing to note about a Lowe index is that the quantity vector qX does
not belong to either of the periods in the comparison (see the International Labour
Organizationʼs CPI manual, 2004, Chapters 9 and 15).
The BLS has responded to the problem of not having up-to-date expenditure
weights by releasing a retrospective chained Törnqvist version of the CPI one year
after the ʻLaspeyresʼ CPI (see Cage, Greenlees and Jackman 2003). Shapiro and
Wilcox (1997) suggest an alternative approach that makes use of the Lloyd (1975)Moulton (1996) price index, defined below.
1− σ 1 / (1− σ )
N ⎡
⎛ pt + k , n ⎞ ⎤
LM
(17)
Lloyd-Moulton: Pt , t + k = Σ ⎢ st , n ⎜
⎟ ⎥
n =1
⎢⎣ ⎝ pt , n ⎠ ⎥⎦
Lloyd-Moulton reduces to a Laspeyres index when σ is equal to zero. The parameter
σ can be interpreted as the elasticity of substitution between pairs of commodities
in the basket. The substitution bias of a Laspeyres index is a direct consequence
of the fact that it sets σ equal to zero. One important feature of the Lloyd-Moulton
index that it shares with the Laspeyres index is that, given a value of σ, it can be
computed without the expenditure data of the current period. Shapiro and Wilcox
experiment with different values of σ, and find that when set to 0.7, the LloydMoulton index approximates quite closely a Törnqvist index for their data set. It
148
Robert J Hill
is unrealistic, however, to assume that the elasticity of substitution does not vary
across pairs of commodities. Nevertheless, short of estimating a whole demand
system, the Lloyd-Moulton index provides a useful alternative to Laspeyres for
computing the headline CPI.
4.
Fixed-base versus Chained Price Indices
All the index number formulae considered above (including all the superlatives)
are intransitive. For example, consider the following three ways of making a
comparison between 2000 and 2002, using the Fisher formula:
P00F,02 – a direct comparison
P00F,01 × P01F,02 – a chained comparison through 2001
P00F,95 × P95F,02 – a chained comparison through 19
995
The fact that bilateral price indices are intransitive implies that each price index
chain is path-dependent, and hence will generate a different answer. This has
important implications for the measurement of inflation. It implies that the resulting
price index series will depend both on the choice of index formula and on the way
the time periods are linked together. To avoid internal inconsistencies, there should
be one, and only one, path between each pair of time periods. This means that the
time periods, when linked together, should form a spanning tree (see RJ Hill 2001).
Three examples of spanning trees are shown in Figure 1. Each vertex in a spanning
tree here denotes one of the time periods in the comparison. Each edge denotes a
bilateral comparison between a pair of time periods.
Figure 1: Examples of Spanning Trees
A fixed-base price index compares every period directly with the base period.
This implies using a star spanning tree with the fixed base at the centre of the star
(the tree on the left in Figure 1). A chained price index compares each period directly
with the period chronologically preceding it. This implies using a spanning tree
like the middle one in Figure 1, with the vertices ordered chronologically. Hence,
it can be seen that the debate over fixed-base versus chained price indices is really
a debate over the choice of spanning tree. A number of intermediate scenarios are
also possible where, for example, the price index could be rebased, say, every five
years. This spanning tree is depicted in Figure 2.
Inflation Measurement for Central Bankers
149
Figure 2: A Hybrid of the Star and Chain Spanning Trees: A Price
Index that Rebases Every Five Years
1984
1994
1989
1988
1983
1980
1982
1999
1995
1997
1992
1981
2003
1990
1985
1987
2004
1998
1993
1986
2000
2002
1991
1996
2001
Something resembling a consensus has emerged in the index-number literature
that price indices should be rebased every year. This tends to minimise the sensitivity
of the results to the choice of price index formula. This sensitivity can be measured
by the spread between Laspeyres and Paasche indices. Generally, the closer the two
time periods being compared, the smaller is the substitution or representativity bias
of Laspeyres and Paasche indices and hence the closer they are together. However,
for quarterly non-seasonally adjusted data the case for chronological chaining is
less clear cut. In this case it is not clear whether March 2002 will be more similar
to June 2002 or to March 2003 (see RJ Hill 2001). Two examples of spanning trees
that annually chain quarterly data are depicted in Figure 3.
Figure 3: Examples of Spanning Trees that Annually Chain
Quarterly Data
M1
J1
M2
J2
S1
D1
M3
J3
S2
M4
S3
D2
J4
S4
D3
D4
J5
S5
D5
M1
M2
M3
M4
M5
J1
J2
J3
J4
J5
S1
S2
S3
S4
S5
D1
D2
D4
D5
D3
M5
Note: M, J, S and D denote March, June, September and December.
150
Robert J Hill
Von der Lippe (2001) has criticised chaining on the grounds that it does not
compare like with like. For example, a comparison between 2000 and 2003 is made
by chaining together comparisons between 2000 and 2001, 2001 and 2002, and
between 2002 and 2003. This means that, irrespective of the choice of formula, the
comparison cannot be reduced to the pricing of a reference basket over two time
periods. Von der Lippe forgets, however, that even a fixed-base comparison uses
chaining, unless we are only interested in comparisons that involve the base year.
Suppose, for example, that we wish to compare 2002 and 2003, when the fixed base
is 1995. This implies chaining together comparisons between 2002 and 1995, and
between 1995 and 2003. In general, it makes more sense if the intermediate links in
the chain lie chronologically in between the two end points. This, by construction,
is always true for a chronological chain, but is not true for a fixed-base price index
when the two periods being compared lie on the same side of the fixed base.
5.
Quality Change and New Goods
The two biggest sources of bias in the CPI identified by the Boskin et al (1996)
report are new goods and quality change. New goods introduce an upward bias
into the CPI (relative to a measure of the COLI) for two reasons. First, when a
new good appears on the market, this in itself represents a price fall. Hicks (1940)
argued that we should view the price in the period before a new good is introduced
as the minimum price at which demand is zero. He referred to this price as the
reservation price. Therefore, when a new good first appears, we can interpret its
price as falling from the reservation price to its initial selling price. This reservation
price can be estimated econometrically. For example, Hausman (1997) estimates
that the reservation price of Apple Cinnamon Cheerios was about double the actual
price when they first appeared on the market. Second, it typically takes a number of
years for new goods to find their way into the CPI basket. This causes an upward
bias since new goods tend to fall significantly in price after they are first introduced.
Hausman (1999), for example, observes how mobile phones were included for the
first time in the US CPI in 1998, even though they first appeared in 1983. By the
end of 1997, there were 55 million mobile phones in use in the US. This second
source of new goods bias in general will exceed the first, since the initial level of
expenditure on new goods is typically small and hence the initial fall in price (from
the reservation level) when the new good first appears should get a small weight
in the CPI.
Quality change arises when a firm produces/provides a new improved version of
a product/service. Frequently there is no overlap between the two versions. That is,
the old version is discontinued as soon as the new version appears. Nevertheless,
statistical agencies try to splice the two price series together often without making
any adjustment for improved quality. Even when the old and new versions overlap the
splicing process is not straightforward. Suppose, for example, that the new and old
versions overlap for a single period (say period 2). Then the price index comparing
periods 1 and 2 depends only on price movements in the old version, while the price
index comparing periods 2 and 3 depends only on price movements in the new
version. This situation can be illustrated with a simple numerical example.
Inflation Measurement for Central Bankers
151
Old version: p1 = 10, p2 = 9.
New version: p2 = 12, p3 = 8.
These price series can be spliced together as follows:
p1 = 10, p2 = 9, p3 = 6.
The problem is that nowhere in this approach is the superior quality of the new
model captured, thus creating an upward bias in the price index (see Nordhaus 1998,
p 61).
Recently there has been a huge upsurge of interest in hedonic regression methods,
as a way of capturing these quality improvements (see, for example, Silver 1999,
Hulten 2003, and Pakes 2003). A hedonic model regresses the price of a product
on its characteristics, some of which may take the form of dummy variables. For
example, consider the case of personal computers (PCs). Three characteristics that
affect the quality of a PC are its speed (MH), RAM and hard drive (GB). If we
have information on the price at which computer i is sold in period t (pti) and the
characteristics of each computer (that is, speed, RAM and hard drive), we can then
run the following regression:
T
ln pti = α + β MH ln MH ti + β RAM ln RAM ti + βGB ln GBti + Σ δ k dkti + ε ti
k =1
(18)
The dkti terms are dummy variables. That is dkti = 1 if t = k and dkti = 0 otherwise.
Once the parameters α, βMH, βRAM, βGB, δ1...δT have been estimated, it is then possible
to specify any combination of the characteristics, and obtain an estimate of the
quality-adjusted price, even if no computer in that particular period had exactly
this combination of characteristics. Our main focus of interest, however, is in the
δk parameters since these are equal to the logarithms of the quality-adjusted price
indices for each period k. There are a number of technical issues that arise in the
construction of hedonic price indices, such as the weighting of different models,
and the choice of characteristics and functional form (for example, semi-log versus
log-log). Nevertheless, it has clearly emerged in recent years as the method of choice
for quality-adjusting price indices.
The BLS started applying hedonic methods to the US CPI for the apparel
category in the early 1990s. Since 1999, hedonic adjustments have also been
made to computers and televisions (see Fixler et al 1999). Hedonic adjustments
are now also being made for microwave ovens, refrigerators, camcorders, VCRs,
DVDs, audio products, college textbooks, and washing machines (see Schultze and
Mackie 2002). The BLS has probably gone further than any other statistical office
in the extent of its quality adjustments. It is no coincidence that it is also one of the
strongest advocates of the COLI.
There has been some debate as to whether some hedonic adjustments used by
the BLS could have gone too far (see Triplett 1999, Harper 2003, and Feenstra and
Knittel 2004). Harper, in particular, argues that insufficient attention may have
been paid to the role of obsolescence. Returning to the example of an old and new
version of a product that overlap for a single period, the price of the old version
may fall in its final period on the market. Buyers will only buy at a discount since
152
Robert J Hill
they now have a better outside option (the new version), and sellers are trying to
unload their stock. To the extent that the price fall is caused by obsolescence, this
means that part of the quality improvement will be captured by the spliced price
index. Failure to account for this obsolescence effect could result in price indices
being over-adjusted for quality change. It remains to be seen how big an issue this
is in practice.
The most intractable quality-adjustment issues arise in the health sector. At
present, what is measured in the CPI is the price of inputs such as a consultation
with a doctor, or of a hospital stay rather than the price of outputs such as a treatment
or attaining a certain health outcome. The reservation price of a health outcome
that was previously unattainable may be very high, and hence a quality-adjusted
medical price index could be significantly lower than the current index included in
the CPI (see Cutler et al 1998).
One important implication for central banks of the more rapid introduction of
new goods into the CPI and the widespread adoption of hedonic adjustment methods
by national statistical offices is that it may cause an implicit change in the rate of
measured inflation. The adoption of hedonic quality-adjustment methods could cause
significant downward adjustments to CPI inflation. If there is no corresponding
adjustment to the central bankʼs inflation target, this will imply a loosening of monetary
policy. For this reason it is important that central banks keep abreast of statistical
innovations that are introduced at their respective national statistical offices.
6.
The Treatment of Owner-occupied Housing in the CPI
Owner-occupied housing is the biggest single component of the CPI in most
countries. It is also one of the most contentious components. Two main approaches
are in use. Australia and New Zealand use the acquisitions approach. The European
Union will probably soon also adopt the acquisitions approach in its HICP (at present
owner-occupied housing is excluded from the HICP). Most other countries use the
rental-equivalence approach. A third approach, referred to as the user-cost approach,
is used by Iceland (see Diewert 2002).
The acquisitions approach is perhaps the easiest to explain. It measures the
cost of constructing new dwellings. Two features of this approach warrant further
discussion. First, the focus on new dwellings is standard in a CPI context. The CPI
does not attempt to track the prices of second-hand goods that are traded between
households. Such transactions can be viewed as transfers between households and
not a net cost incurred by the household sector. It is for this reason that sales of
second-hand cars are also excluded from the domain of the CPI. Far more contentious
is the fact that the acquisitions approach only measures the cost of constructing a
new dwelling. That is, changes in land prices are ignored. Again, this approach can
be justified on the grounds that the land is not new.
The rental-equivalence approach, by contrast, attempts to impute the rent that
an owner occupier would earn if she rented out her house rather than live in it. The
total value of this imputed rent across all home-owning households is then included
in the CPI. In practice, these imputed rents must be estimated from data obtained
Inflation Measurement for Central Bankers
153
from the actual rental market. This can be problematic if the rental market is thin
or if the characteristics of owner-occupied and rental properties do not match (see
Kurz and Hoffman 2004). To get round these problems, in the US home owners are
surveyed directly and asked to estimate the rent they could receive for their homes
(see Ewing, Ha and Mai 2004).
This same issue arises for all consumer durables, of which housing is just one
example (although admittedly a very important one). The CPI could track the price
of a new consumer durable (that is, the acquisitions approach) or the cost of the
services it provides each period (that is, the rental-equivalence approach). These two
approaches will give different answers. In the case of housing, the difference can be
large. This is because land prices are, to some extent, implicitly included under the
rental-equivalence approach. The exact interaction depends on how rents react to
changes in land prices. Irrespective of the exact nature of this interaction, the total
expenditure share of owner-occupied housing is larger under a rental-equivalence
approach than under an acquisitions approach, and the housing price index itself
is much more responsive to changes in land prices. The impact of the choice of
approach on the observed expenditure share of owner-occupied housing can be
observed to some extent from comparisons across countries. The US and Canada
use the rental-equivalence approach. The expenditure share of owner-occupied
housing in the US and Canada is about 23 per cent and 18 per cent, respectively.
The corresponding expenditure shares for Australia and New Zealand (based on
the acquisitions approach) are about 11 per cent and 14 per cent, respectively (see
Ewing et al 2004).
The case of owner-occupied housing again illustrates two important points.
First, a national statistical officeʼs stance on the COGI versus COLI debate is a
good predictor of its treatment of owner-occupied housing. Statistical offices that
prefer the COGI concept tend to use the acquisitions approach, while those that
prefer the COLI tend to use the rental-equivalence approach. It must be emphasised,
however, that the rental-equivalence approach is in no way inconsistent with the
COGI concept which, it must be remembered, tracks the prices of services as well
as goods. Second, the behaviour of the CPI over time can be highly sensitive to the
underlying methodologies used in its construction. These can differ from one country
to the next, and can change in each country over time. For an inflation-targeting
regime to function effectively, it is necessary that central banks keep abreast of
these methodological issues.
7.
Inflation Targeting in the European Union
The creation of the European Central Bank (ECB) necessitated the construction
of a harmonised index of consumer prices (HICP) for the member countries of the
European Union. This was something of a logistical nightmare given the significant
differences in the methodologies used by the member countries to construct their own
CPIs. The treatment of owner-occupied housing is a case in point. It ended up being
put in the ʻtoo hardʼ category and at present is completely excluded, although in the
next few years it will probably be included on an acquisitions basis (see Astin 1999).
154
Robert J Hill
Given its large share in total consumer expenditure (even on an acquisitions basis)
this could cause a structural break in the HICP, particularly given that house prices
are rising faster than the HICP in many EU countries.
The adoption of an inflation target for the euro area has been made more difficult
by the widely differing inflation rates across the member countries. Differing inflation
rates within the euro area means that monetary policy may be too stimulative in
some countries and too restrictive in others. This problem could become more severe
when the euro area is widened to include relatively low-price countries in Eastern
Europe. This problem is probably an inevitable consequence of the creation of a
single market with a common currency, since it is causing a convergence of price
levels across countries (see Rogers 2001, RJ Hill 2004). That is, poorer, more labourintensive countries (for example, Greece, Portugal and Spain) generally have lower
price levels since non-tradables, in general, are more labour intensive and hence
relatively cheaper (see Kravis and Lipsey 1983, and Bhagwati 1984). Increased
labour and firm mobility is acting to reduce these differences, thus causing higher
rates of inflation in these countries. Lower-inflation countries (such as Germany)
are therefore burdened with higher interest rates than might otherwise be deemed
desirable.
8.
Scanner Data
It was stated earlier that ideally the CPI should be constructed using the Fisher,
Törnqvist or Walsh formulae. One drawback of each of these formulae is that
it requires expenditure data for the current period. At present such data are not
generally available. The expenditure shares are typically obtained from household
expenditure surveys, that in some countries are only undertaken at five- or even tenyear intervals. National statistical offices in most countries are more or less forced
to use the Laspeyres formula, with the base year updated whenever the results of a
new household expenditure survey become available. Furthermore, the expenditure
data are only available at an aggregated level. For example, the Australian CPI only
has expenditure data on 89 headings (see ABS 2000). Examples of these headings
include milk, cheese, bread, and breakfast cereals.
This situation could change dramatically in the next few years due to the
increased availability of scanner data. AC Nielson collects records of transactions
at supermarkets, department stores and other shops. This has the potential to
revolutionise the CPI in two ways. First, expenditure data will be available at the
level of individual commodities. Second, both the price and expenditure data will
be available almost continuously. Admittedly, this is only true for certain parts of
the CPI, particularly food, beverages and clothing. It means, however, that at least
for these components, the CPI can be computed weekly (or even daily) using a
superlative formula such as Fisher. Third, scanner data can also be used in hedonic
regressions to obtain more accurate estimates of quality change and better matching
of characteristics and of products across geographical locations.
With these benefits also come problems. More disaggregated data tend to exhibit a
stronger substitution effect. For example, a consumer is much more likely to substitute
Inflation Measurement for Central Bankers
155
between two different brands of beer when relative prices change, than between
beer and wine. A stronger substitution effect implies that the resulting price index
will be more sensitive to the choice of formula. Reinsdorf (1999) and Feenstra and
Shapiro (2003) document evidence of huge shifts in expenditure driven by sales on
coffee and canned tuna, respectively. This is particularly troubling for chained price
indices. For example, consider the case of a weekly chained Laspeyres price index
for a particular supermarket. Suppose further that one brand of coffee is put on sale
for one week (in week 2), and that this results in a huge increase in expenditure on
this brand for the duration of the sale. The weekly chained Laspeyres index will give
too little weight to the fall in the price in the coffee brand in week 2, and too much
weight to its increase in price in week 3, both of which will create an upward bias.
A fixed-base Laspeyres index, by contrast, will only be affected by the first of these
biases and hence will have a smaller overall bias. By similar reasoning it follows that
a weekly chained Paasche index could have a stronger downward bias than a fixedbase Paasche index. Although chained Fisher should be free of substitution bias, the
large biases in chained Laspeyres and Paasche indices (remembering that Fisher is
the geometric mean of Laspeyres and Paasche) may cause it to be somewhat erratic.
Reinsdorf indeed finds evidence of erratic movements in chained Fisher indices
for the case of coffee. The findings of Feenstra and Shapiro (2003) are even more
surprising. For the case of canned tuna, they find that even the chained Törnqvist
index has an upward bias. This is surprising since like all other superlative indices
it satisfies the time-reversal test (see Balk 1995). They attribute the bias to the fact
that sales are only advertised towards the end of the period, and hence there is a
large spike in expenditure just before the sale ends. This means that the rise in the
price of tuna when the sale ends has a much bigger effect on the index than the fall
in price when the sale begins.
A number of national statistical offices have started experimenting with scanner
data with the intention of eventually incorporating them into their CPIs. The
experiences of Statistics Netherlands and the ABS are discussed in van Mulligen
and Oei (forthcoming) and Jain and Caddy (2001), respectively. The paper by
Reinsdorf (1999) is part of a broader project on the properties of scanner data at
the BLS in the US.
From a central banking perspective, scanner data raise two main issues. First,
there is the question of how frequently the CPI should be computed. The frequency
varies across countries from monthly to quarterly. Scanner data, however, open up
the possibility of computing a weekly CPI. It is not clear whether a central bank
should be in favour of such a development, particularly if in the process, the CPI
becomes more volatile. The increased volatility of the CPI at existing frequencies
is the second issue. The use of scanner data will almost certainly increase volatility
since it captures the strong substitution effects that occur at the level of individual
commodities. More research is required to determine the best ways of handling
scanner data. As was noted above, it is already clear that such indices should not
be chained weekly. Nevertheless, it is only a matter of time until national statistical
offices start using scanner data in their CPIs. Central banks, therefore, should start
thinking about the implications of scanner data for inflation targeting.
156
9.
Robert J Hill
Conclusion
Inflation targeting has been remarkably successful at bringing down inflationary
expectations in most countries that have adopted it. There has been much debate
regarding what rate of inflation a central bank should be targeting, and on methods
for forecasting the rate of inflation so that a central bank can anticipate future trends
and better meet its target. One aspect of the inflation-targeting regime, however,
that has perhaps been somewhat neglected in the literature is the choice of the target
price index itself. It is by no means clear that the CPI is the ideal target. The CPI
in most countries was designed as a benchmark for adjusting public and private
sector wages rather than as a monetary policy benchmark. Some researchers have
argued that, in an inflation-targeting context, the focus of the CPI is too narrow
since it ignores prices of a range of items, such as investment goods, public-sector
goods and services, exports, and assets such as land and equities. In contrast, other
researchers have argued that its focus is too broad, and that volatile elements such
as some, or all, food and energy prices should be excluded.
Even supposing that we agree on the CPI as the inflation target, a national
statistical office must still make a number of decisions that can significantly affect
the index. First, there is the matter of whether the statistical office views the CPI as
a COGI or COLI. This decision need not, in and of itself, necessarily have a major
impact. However, in practice, it usually does, since it sets the tone with regard to
the number of imputations included in the index. Two key types of imputations are
made in the CPI. The first type are quality-adjustments, particularly to computers,
televisions, microwave ovens, refrigerators, VCRs, DVDs, washing machines,
cars and in the health sector. These adjustments are usually made using hedonic
regression methods. The second type of imputation is the treatment of owner-occupied
housing. Statistical offices that adopt the COLI concept tend to make more quality
adjustments (potentially making the CPI lower than it would otherwise be, by as
much as 1 percentage point, using the Boskin report as a rough guide), and tend
to use the rental-equivalence approach for owner-occupied housing. When house
prices are rising faster than the CPI excluding housing, then the use of the rentalequivalence approach will tend to make the CPI rise faster than if the acquisitions
approach (generally preferred by advocates of the COGI) is used. It is important,
therefore, that each central bank keeps abreast of the imputations its statistical
office is including in the CPI, and in particular of any changes in methodology that
might affect the index. Failure to do so could result in inadvertent changes in the
stance of monetary policy. For example, if a statistical office suddenly expands its
quality-adjustment program, this may require a central bank to lower its inflation
target to avoid a loosening of monetary policy.
Looking forward, scanner data have the potential to revolutionise the construction
of the CPI by providing far more detailed expenditure weights at far greater frequency
than are currently available. The incorporation of scanner data into the CPI may
make the index more volatile as well as allowing it to be computed more frequently
(for example, on a weekly basis). It might be prudent for central banks also to start
considering how the use of scanner data in the CPI might affect the operation of an
inflation-targeting regime.
Inflation Measurement for Central Bankers
157
References
Astin J (1999), ʻThe European Union harmonised indices of consumer prices (HICP)ʼ,
Statistical Journal of the United Nations Economic Commission for Europe, 16(2-3),
pp 123–135.
Australian Bureau of Statistics (ABS) (2000), A guide to the consumer price index: 14th series,
Cat No 6440.0.
Balk BM (1995), ʻAxiomatic price index theory: a surveyʼ, International Statistical Review,
63(1), pp 69–93.
Bhagwati JN (1984), ʻWhy are services cheaper in the poor countries?ʼ, Economic Journal,
94(374), pp 279–286.
Blinder AS (1997), ʻCommentary on “Measuring short-run inflation for central bankers” by
SG Cecchettiʼ, Federal Reserve Bank of St. Louis Review, 79(3), pp 157–160.
Bloem AM, PA Armknecht and KD Zieschang (2002), ʻPrice indices for inflation targetingʼ,
paper presented at the International Monetary Fund Seminar on the Statistical
Implications of Inflation Targeting, Washington DC, February 28–March 1.
Boskin MJ, ER Dulberger, RJ Gordon, Z Griliches and D Jorgenson (1996), Toward a more
accurate measure of the cost of living, Final Report to the Senate Finance Committee from
the Advisory Commission to Study the Consumer Price Index, Washington DC.
Cage R, J Greenlees and P Jackman (2003), ʻIntroducing the chained consumer price
indexʼ, paper presented at the Seventh Meeting of the Ottawa Group International
Conference on Price Indices, Paris, 27–29 May. Available at <http://www.bls.gov/
cpi/super_paris.pdf>.
Cecchetti SG (1997), ʻMeasuring short-run inflation for central bankersʼ, Federal Reserve
Bank of St. Louis Review, 79(3), pp 143–155.
Cutler D, MB McClellan, JP Newhouse and D Remler (1998), ʻAre medical prices declining?
Evidence from heart attack treatmentsʼ, Quarterly Journal of Economics, 113(4),
pp 991–1024.
Deaton A (1998), ʻGetting prices right: what should be done?ʼ, Journal of Economic
Perspectives, 12(1), pp 37–46.
Diewert WE (1976), ʻExact and superlative index numbersʼ, Journal of Econometrics, 4,
pp 114–145.
Diewert WE (1996), ʻSeasonal commodities, high inflation and index number theoryʼ,
Department of Economics, University of British Columbia Discussion Paper
No 96-06.
Diewert WE (2002), ʻHarmonized indices of consumer prices: their conceptual foundationsʼ,
Swiss Journal of Economics and Statistics, 138(4), pp 547–637.
Ewing I, Y Ha and B Mai (2004), ʻWhat should the consumer price index measure?ʼ,
Statistics New Zealand, Consumers Price Index Revision Advisory Committee 2004
Discussion Paper.
Feenstra RC and CR Knittel (2004), ʻRe-assessing the US quality adjustment to computer
prices: the role of durability and changing softwareʼ, paper presented at the CRIW
Conference on Index Theory and Measurement of Prices and Productivity, Vancouver,
28–29 June.
158
Robert J Hill
Feenstra RC and MD Shapiro (2003), ʻHigh-frequency substitution and the measurement of
price indicesʼ, in RC Feenstra and MD Shapiro (eds), Scanner data and price indices,
University of Chicago Press, Chicago, pp 123–146.
Feldstein M (1997), ʻThe costs and benefits of going from low inflation to price stabilityʼ,
in CD Romer and DH Romer (eds), Reducing inflation: motivation and strategy,
University of Chicago Press, Chicago, pp 123–156.
Fixler D, C Fortuna, J Greenlees and W Lane (1999), ʻThe use of hedonic regressions to
handle quality change: the experience in the US CPIʼ, paper presented at the Fifth
Meeting of the Ottawa Group International Conference on Price Indices, Reykjavik,
25–27 August.
Goodhart C (2001), ʻWhat weight should be given to asset prices in the measurement of
inflation?ʼ, Economic Journal, 111(472), pp F335–F356.
Harper MJ (2003), ʻTechnology and the theory of vintage aggregationʼ, paper presented at the
NBER Conference on Hard-to-measure Goods and Services in Honor of Zvi Griliches,
Bethesda, Maryland, 19–20 September.
Hausman JA (1997), ʻValuation of new goods under perfect and imperfect competitionʼ,
in TF Bresnahan and RJ Gordon (eds), The economics of new goods, University of
Chicago Press, Chicago, pp 209–237.
Hausman JA (1999), ʻCellular telephone, new products, and the CPIʼ, Journal of Business
and Economic Statistics, 17(2), pp 188–194.
Hicks JR (1940), ʻThe valuation of the social incomeʼ, Economica, 7, pp 105–124.
Hill RJ (2001), ʻMeasuring inflation and growth using spanning treesʼ, International Economic
Review, 42(1), pp 167–185.
Hill RJ (2004), ʻConstructing price indices across space and time: the case of the European
Unionʼ, American Economic Review, forthcoming.
Hill RJ (forthcoming), ʻSuperlative index numbers: not all of them are superʼ, Journal of
Econometrics.
Hill TP (1996), Inflation accounting: a manual on national accounting under conditions of
high inflation, OECD, Paris.
Hill TP (1998), ʻThe measurement of inflation and changes in the cost of livingʼ, Statistical
Journal of the United Nations Economic Commission for Europe, 15, pp 37–51.
Hulten CR (2003), ʻPrice hedonics: a critical reviewʼ, Federal Reserve Bank of New York
Economic Policy Review, 9(3), pp 5–15.
International Labour Organization (ILO) (2004), CPI manual, ILO Bureau of Statistics,
Geneva. A preliminary draft of the manual is available at <http://www.ilo.org/public/
english/bureau/stat/guides/cpi>.
International Monetary Fund (IMF) (2004), PPI manual, IMF, Washington DC.
A preliminary draft of the manual is available at <http://www.imf.org/external/np/
sta/tegppi/index.htm>.
Jain M and J Caddy (2001), ʻUsing scanner data to explore unit value indicesʼ, paper presented
at the Sixth Meeting of the Ottawa Group International Conference on Price Indices,
Canberra, 2–6 April.
Kohli U (1983), ʻTechnology and the demand for importsʼ, Southern Economic Journal,
50, pp 137–150.
Inflation Measurement for Central Bankers
159
Konüs AA (1939), ʻThe problem of the true index of the cost of livingʼ, trans J Bronfenbrenner,
Econometrica, 7, pp 10–29. Originally published in Russian in 1924.
Kravis IB and RE Lipsey (1983), ʻToward an explanation of national price levelsʼ, Princeton
Studies in International Finance No 52.
Kurz C and J Hoffmann (2004), ʻA rental-equivalence index for owner-occupied housing
in West Germany 1985 to 1998ʼ, Deutsche Bundesbank Discussion Paper Series 1:
Studies of the Economic Research Centre No 08/2004.
Lloyd PJ (1975), ʻSubstitution effects and biases in nontrue price indicesʼ, American Economic
Review, 65(3), pp 301–313.
Moulton BR (1996), ʻConstant elasticity cost-of-living index in share-relative formʼ, Bureau
of Labor Statistics, mimeo.
Nordhaus WD (1998), ʻQuality change in price indicesʼ, Journal of Economic Perspectives,
12(1), pp 59–68.
Pakes A (2003), ʻA reconsideration of hedonic price indices with an application to PCʼsʼ,
American Economic Review, 93(5), pp 1578–1596.
Pollak RA (1981), ʻThe social cost-of-living indexʼ, Journal of Public Economics, 15(3),
pp 311–336.
Pollak RA (1989), The theory of the cost-of-living index, Oxford University Press,
New York.
Reinsdorf MB (1999), ʻUsing scanner data to construct CPI basic component indicesʼ,
Journal of Business and Economic Statistics, 17(2), pp 152–160.
Rogers JH (2001), ʻPrice level convergence, relative prices, and inflation in Europeʼ, Board
of Governors of the Federal Reserve System, International Finance Discussion Paper
No 699.
Schultze C and C Mackie (eds) (2002), At what price? Conceptualizing and measuring
cost-of-living and price indices, report of the Panel on Conceptual, Measurement, and
Other Statistical Issues in Developing Cost-of-Living Indices, The National Academies
Press, Washington DC.
Shapiro MD and DW Wilcox (1997), ʻAlternative strategies for aggregating prices in the
CPIʼ, Federal Reserve Bank of St. Louis Review, 79(3), pp 113–125.
Silver M (1999), ʻAn evaluation of the use of hedonic regressions for basic components of
consumer price indicesʼ, Review of Income and Wealth, 45(1), pp 41–56.
Silver M and C Ioannidis (2001), ʻIntercountry differences in the relationship between
relative price variability and average pricesʼ, Journal of Political Economy, 109(2),
pp 355–374.
Tatom JA (2002), ʻStock prices, inflation and monetary policyʼ, Business Economics, 37(4),
pp 7–19.
Triplett JE (1999), ʻThe Solow computer paradox: what do computers do to productivity?ʼ,
Canadian Journal of Economics, 32(2), pp 309–334.
Triplett JE (2001), ʻShould the cost-of-living index provide the conceptual framework for a
consumer price index?ʼ, Economic Journal, 111(472), pp F311–F334.
van Mulligen PH and MH Oei (forthcoming), ʻThe use of scanner data in the CPI: a curse
in disguise?ʼ, Statistics Netherlands Discussion Paper.
160
Robert J Hill
von der Lippe PM (2001), Chain indices, a study in price index theory, Vol 16 of the Publication
Series ʻSpectrum of Federal Statisticsʼ, Statistisches Bundesamt, Wiesbaden.
Woolford K (1999), ʻMeasuring inflation: a framework based on domestic final purchasesʼ, in
M Silver and D Fenwick (eds), Proceedings of the measurement of inflation conference,
Cardiff Business School, Wales, pp 518–534.